Operations with Polynomials and Factoring Polynomials

Add/Subtract Polynomials

100

Add:

(4x² + 2x) + (x² + 6x)

Answer:  

(4x² + 2x) + (x² + 6x) =  

5x² +8x

Combine LIKE terms

200

Subtract:  

(-3a² - 2a) - (4a² - 4)

Answer:  

(-3a² - 2a) - (4a² - 4) =  

-7a² - 2a + 4

 keep-change-opposite

300

Add:  

(5r³ - 6r² + 3r - 9) + (r² - 2r - 3)

Answer: 

(5r³ - 6r² +3r - 9) + (r² -2r - 3) =  

5r³ - 5r² + r - 12

combine LIKE terms

400

Subtract:  

(- 2x² - x  + 4 ) - (x² + 3x - 2)

Answer: 

(- 2x² - x  + 4 ) - (x² + 3x - 2) = 

-3x² - 4x + 6

keep-change-opposite

Multiplying Polynomials

100

Multiply:

5x² (2x - 8)

Answer:  

5x² (2x - 8)  =

 10x³ - 40x² 

Distributive Property (add exponents!) 

200

Multiply:

(n + 3)(n + 7)

Answer:  

(n + 3)(n + 7) =

 n² + 10n + 21

Double Distributive/FOIL Method

300

Multiply:

(x + 4)(x - 10)

Answer:  

(x + 4)(x - 10) =    

x² - 6x - 40

Double Distributive/FOIL Method

400

Multiply:

(5x - 3)(2x - 7)

Answer:  

(5x - 3)(2x - 7) =    

10x² - 41x + 21

Double Distributive/FOIL Method

500

Multiply: 

(2x+ 5)² 

Answer: 

(2x+ 5)²  = (2x+ 5) (2x+ 5)

4x² + 20x + 25

FOIL / Double Distributive (write out the problem!) 

Factoring GCF

100

The GCF of 30x⁴  and 25x²

Answer:  

What is 5x²

(GCF of 30x⁴  and 25x²) 

200

Factor:  (Hint: use GCF) 

 12x³ + 16x²   

Answer:  

12x³ + 16x² =    

4x²(3x + 4)

Factor out the GCF

300

Factor:  (Hint: use GCF)

18x⁴ + 2x² - 6x  

Answer:  

18x⁴ + 2x² - 6x  = 

2x (9x³ + x - 3) 

Factor out the GCF

400

Factor:  (Hint: use GCF)

50x²y⁴- 40xy⁷

Answer:  

50x²y⁴- 40xy⁷  = 

10xy⁴ (5x - 4y³) 

Factor out the GCF

500

Factor completely: 

24x³-6x

Answer:  

24x³ - 6x  =  6x(4x² - 1)

6x(2x + 1) (2x - 1)   

GCF then DOTS

Factoring DOTS

100

Factor: 

x² - 36

Answer:  

x² - 36 =

(x + 6)  (x - 6)  

Difference of Two Squares

200

Factor:

4x² - 9

Answer:  

4x² - 9 =

(2x + 3)  (2x - 3)  

Difference of Two Squares

300

Factor:

16x² - 49y²

Answer:  

16x² - 49y²=

(4x + 7y)  (4x - 7y)  

Difference of Two Squares

400

Factor COMPLETELY:

25x² - 100

Answer:  

25x² - 100  =  25(x² - 4)  

25(x + 2)  (x - 2)  

GCF then Difference of Two Squares

500

Factor Completely:  

2x⁴ - 32 

What is 

2 (x²+4) (x+2) (x-2)

GCF then DOTS twice: 2(x⁴- 16) = 

2 (x²+4) (x²-4) = 

2 (x²+4) (x+2) (x-2)

Factoring Trinomials

100

Factor:

x² + 8x + 12

Answer:  

x² + 8x + 12  =  

(x + 6)  (x + 2)  

unFOIL  

(2 numbers whose product is 12 and sum is 8)

200

Factor: 

m² - 11m + 18

Answer:  

m² - 11m + 18   =  

(m - 9)  (m - 2)  

unFOIL  

(2 numbers whose product is 18 and sum is -11)

300

Factor: 

x² + 5x - 24

Answer:  

x² + 5x - 24    =  

(x + 8) (x - 3) 

unFOIL  

(2 numbers whose product is -24 and sum is 5)

400

Factor: 

y² - 6y - 7

Answer:  

y² - 6y - 7    =  

(y - 7)(y + 1)

unFOIL  

(2 numbers whose product is -7 and sum is -6)

500

Factor completely: 

2n³ - 10n² - 28n

Answer:  

2n³ - 10n² - 28n   =  2n (n² - 5n - 14) 

2n(n - 7) (n + 2)  

GCF then unFOIL  

(2 numbers whose product is -14 and sum is -5)